Container closure machines for closing bottles or other containers are known in various embodiments. In particular container closure machines are known for closing bottles or other containers with screw caps. These caps are applied to the containers by screwing onto an external thread provided in the area of the container opening concerned, namely by screwing with a closure tool which is equipped with a closure head forming a receptacle for the respective closure. In detail, the container concerned is closed such that the respective cap is first held in the receptacle of the closure head. Then the cap held in the closure head at least by force-fit i.e. by clamping, is placed on the container opening and then screwed onto the respective container by the closure head driven rotationally about a closure head axis or receptacle axis. A force-fit connection does not exclude the provision of grooving and/or fluting which allows at least a partial form fit by interlocking of opposing surface contours.